A. MATHEMATICS AND ASTRONOMY. 7 



will come out smaller than the normal refraction. Some 

 changes in the co-efficient of refraction seem to take place so 

 suddenly that they can only be explained by supposing a 

 derangement of the instrument. Excepting these, the re- 

 mainder of the determinations merit great confidence. In 

 general, the formula? of Struve accord very well with these 

 later observations made in the mountains of the Caucasus. 

 The formula proposed by Sawitsch gives the refractions a 

 little too great. Bulletin Acad. ImperiaU des Sciences^ St. 

 Petersburg, 1875,318. 



CELESTIAL PHOTOMETRY. 



Lindemann has investigated the merits of the method of 

 estimating the brightness of stars as taught by Argelander, 

 as compared with the measurements of the stellar-photometer 

 invented by ZoUner. He has chosen to this end to make ob- 

 servations both with the unaided eye and with Zollner's in- 

 strument upon the interesting variable star Algol, or Beta 

 Persei. His observations began in 1870; but in the course 

 of four years he was only able to secure observations of six 

 Algol minimi suitable to his purpose. A review of his work 

 by the eminent observer of variable, stars, Schonfeld, shows 

 that the naked-eye estimates made by Lindemann belong to 

 the best class of work of that nature; and that his observa- 

 tions made by means of Zullner's photometer can not be con- 

 sidered superior, and are even barely equal thereto, so far, 

 at least, as accidental errors are concerned. With regard, 

 however, to systematic differences in these two methods of 

 observation, Lindemann's research yielded the most interest- 

 ing conclusions, as showing that exterior influences appear 

 to affect the instrumental observations less than those with 

 the unaided eye; the latter make the epochs of Algol's min- 

 imum brightness come somewhat earlier than the former, 

 but the photometric measures and the naked-eye estimations 

 agree somewhat better after the minimum has passed than 

 before. By comparison of his own estimates, Schonfeld finds 

 that the diminution of brio-htness before the minimum is 

 reached is, as given by him, slightly greater than that ob- 

 served by Lindemann ; while, on the contrary, after the min- 

 imum has passed, Schonfeld's estimates are lower than those 

 of Lindemann. The observations of Lindemann are a con- 



